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EnglishTail-Risk-Hedging in Emerging-Markets-Währungen
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Wer hat Angst vorm schwarzen Schwan? Tritt ein extrem seltenes Ereignis mit unvorhergesehenen Folgen auf, spricht man von einem schwarzen Schwan. Und ein solcher taucht häufiger auf, als es die Normalverteilung vermuten ließe. Bezogen auf Investitionen – auch in Hochzinswährungen – bedeutet dies, dass es sinnvoll ist, Risikokennzahlen über die historische Verteilung zu ermitteln und Tail-Risiken abzusichern.
Schwarze Schwäne, Event- und Tail-Risks in der Finanzwelt
Spätestens seit der Finanzkrise 2008/2009 steht der schwarze Schwan auch für seltene Ereignisse in der Finanzwelt, mit denen niemand gerechnet hat und die mit sehr hohen Verlusten einhergehen. Diese Ereignisse werden auch als Event-Risk oder auch Tail-Risiko bezeichnet. Das „Tail“ in Tail-Risiko bezieht sich auf die Endabschnitte der glockenförmigen Kurve, die die Wahrscheinlichkeitsverteilung von Ereignissen darstellt. Im Zusammenhang mit Investitionen stellt die äußerste linke Seite der glockenförmigen Verteilung die niedrigsten Renditen dar, die rechte Seite die höchsten Renditen.
Ermittlung von Risikokennzahlen anhand der Normalverteilung
Für das Risiko ist nur die linke Seite der Kurve – der linke Tail – der Verteilung interessant. Die Vermutung, dass hohe Verluste seltene Ereignisse sind, bestand bereits Mitte des vergangenen Jahrhunderts. In der Finanzmathematik wurde für Risikomodelle die Normalverteilung (oder auch logarithmische Normalverteilung) unterstellt. In der Normalverteilung sind die Tails relativ dünn und kurz. So fußt das Standardmodell zur Bewertung von Optionen von Fischer Black und Myron Scholes auf dieser Annahme. Es wurde in den 1970er-Jahren aufgestellt. Der Vater der modernen Portfoliotheorie, Harry Markowitz, entwickelte seine Theorie bereits 1952 und erhielt 1990 dafür den Nobelpreis. Die Normalverteilung der Renditen wurde auch hier zur Vereinfachung angenommen. Und dies vereinfacht die Berechnung erheblich. Durch die Normalverteilung lässt sich das Risiko schnell erfassen. Eine einzige Kennzahl genügt: die Volatilität. Eine Volatilität von 10 % besagt, dass das Wertpapier in 68 % der Fälle um bis zu 10 % im Wert schwankt. In 1 % der Fälle liegt das Verlustrisiko bei 23,3 % oder höher. Dies ist die Kennzahl „Value at Risk“ (VaR 1 %), die heute in keinem Risikoreport fehlt – wenn sie auch in der Regel nicht aus der Normalverteilung gerechnet wird, dazu aber später...
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